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# Statistics and Probability with Applications (High School)

## Fourth Edition| ©2021 Daren Starnes; Josh Tabor; Luke Wilcox

With the power of SaplingPlus online learning behind it, this engaging and modern introduction to statistics helps prepare students for success in this course and in life. Structured into bite-sized lessons with many integrated activities to get students “doing statistics” from the start, t...

With the power of SaplingPlus online learning behind it, this engaging and modern introduction to statistics helps prepare students for success in this course and in life. Structured into bite-sized lessons with many integrated activities to get students “doing statistics” from the start, this program helps students understand the “why” and “how” of statistics. The robust resource program, including student and teacher e-books with resources integrated at point-of-use and online homework with thorough guided feedback makes this the ideal homework for in person or a virtual learning environment.

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Written by HS teachers for HS students.

With the power of SaplingPlus online learning behind it, this engaging and modern introduction to statistics helps prepare students for success in this course and in life. Structured into bite-sized lessons with many integrated activities to get students “doing statistics” from the start, this program helps students understand the “why” and “how” of statistics. The robust resource program, including student and teacher e-books with resources integrated at point-of-use and online homework with thorough guided feedback makes this the ideal homework for in person or a virtual learning environment.

Features

Hundreds of worked examples with step-by-step solutions that feature the “voice of the teacher” through the “teacher talk” boxes. Each Example points to an exercise to practice the concepts. The exercises guide students directly to the supporting example for help when they need it. If they need more help, they can click on the Exercise video that features an experienced High School Statistics teacher walking step-by-step through the solution to the exercise.

Lesson Apps wrap up the learning targets in each example and provide a great review and self-check for students.

Easy to use Statistical **Applets** allow students to do simulations and work with data from their computer, table, phone, or an connected device.

Tech Corners provide keystroke level instruction for using Applets and/or the TI-83/84+ graphing calculator.

STATS applied! Real world problems begin and end each chapter to underscore why understanding statistics is important.

**SaplingPluse+book and media resources + Sapling online homework**

SaplingPlus combines the unparalleled assets of Sapling Learning’s online homework (homework with targeted feedback, superior support for students and instructors) with an e-book and powerful book-specific assets.

New to This Edition

There are now 11 chapters that are more similar in length – with 6-8 lessons in each chapter.

Introduce Normal distributions as models for data **earlier in the book**, to match modern practice.

- Add a new Chapter 2 “Modeling One-Variable Quantitative Data” that focuses on measuring location in a distribution (percentiles, z-scores) and on using Normal distributions to model certain sets of quantitative data. This approach matches the structure of AP texts and most college titles and will feel more familiar to teachers who teach both courses. This move also allows for shortening Chapter 1 (which was 9 lessons in SPA 3e), having Normal distributions available when discussing inference for sampling and inference for experiments in Chapter 3 on Collecting Data, and giving students additional practice and familiarity with the most important distribution in an introductory statistics course.

**Overhauled Sapling Plus online Homework**

- All “suggested assignment” questions from the text with detailed guided feedback to help students learn even when they get the answer wrong are ready to use in Sapling Plus
- Hundreds of additional questions coded by lesson in many different formats – sorting, numerical entry, drop-down menu choice options, open answer - -including many with algorithmic data.
- Improved tutorial help for using the program included in the resource options
**(Sapling Plus will be the course management option for school year 2021-2022, we plan to move into Achieve for school year 2022-2023)**

**Increase students’ focus on solidifying essential knowledge as a precursor to mastering concepts and skills.**

- We have added a new set of exercises at the beginning of each Lesson exercise set called: Building Concepts and Skills. The addition of these 5-7 definition based exercises help the lesson exercises ramp up more effectively from Building Concepts and Skills to Mastering Concepts and Skills to Applying the Concepts to Extending the Concepts, and finally to Recycle and Review, which integrate skills and concepts from previous lessons.

**Expand and refine the video program to support students and teachers more effectively**

**NEW Lesson App Videos**for all 71 Lessons replace the individual Worked Example Videos. Short video lessons, based on the Lesson App in each lesson, review and offer instruction on the key skills and concepts in each lesson by teaching the Lesson App. Prepared by SPA4 TE author, Doug Tyson, and SPA4 Solutions/Assessment/Sapling author, Erica Chauvet, you can be confident in assigning these lessons to students who miss class, are struggling, or just need help bringing the ideas together. They will also provide excellent support for virtual instruction.**NEW Worked Exercise Videos**– each “For Practice, Try” exercise is now available as an instructional video for students. Prepared by a team of experienced high school Stat teachers.**Additional Video support includes:**

PD Videos (for teachers):

- Chapter Overviews (by Daren, Josh, Luke)

- Lesson Overviews (by Daren, Josh, Luke)

- Getting to know the TE (by Doug Tyson)

- Comprehensive Course Tour

For Students (and teachers)

- Lesson App Videos

- Worked Exercise Videos (“For Practice, Try” paired exercises)

- Chapter Review Exercises**NEW comprehensive set of Lecture Presentation Slides**for each Lesson will support teachers more thoroughly in preparing virtual lessons, as needed, and in helping student absences, substitute teachers, etc.**Many new Examples and exercises**with updated, timely, high-interest data.

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**
Statistics and Probability with Applications (High School)**

Fourth Edition| ©2021

Daren Starnes; Josh Tabor; Luke Wilcox

# Digital Options

## SaplingPlus

Get the e-book, do your homework online, try some quizzes, and more!

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**Statistics and Probability with Applications (High School)**

Fourth Edition| 2021

Daren Starnes; Josh Tabor; Luke Wilcox

## Table of Contents

About the Authors

Acknowledgments

To the Student

**Chapter 1 Analyzing One-Variable Data**

Lesson 1.1 Statistics: The Science and Art of Data

Lesson 1.2 Displaying Categorical Data

Lesson 1.3 Displaying Quantitative Data: Dotplots

Lesson 1.4 Displaying Quantitative Data: Stemplots

Lesson 1.5 Displaying Quantitative Data: Histograms

Lesson 1.6 Measuring Center

Lesson 1.7 Measuring Variability

Lesson 1.8 Summarizing Quantitative Data: Boxplots and Outliers

**Chapter 2 Modeling ****One-Variable Quantitative Data**

Lesson 2.1 Describing Location in a Distribution

Lesson 2.2 Transforming Data

Lesson 2.3 Density Curves and the Normal Distribution

Lesson 2.4 The Empirical Rule and Assessing Normality

Lesson 2.5 Normal Distributions: Finding Areas from Values

Lesson 2.6 Normal Distributions: Finding Values from Areas

**Chapter 3 Analyzing Two-Variable Data**

Lesson 3.1 Relationships Between Two Categorical Variables

Lesson 3.2 Relationships Between Two Quantitative Variables

Lesson 3.3 Correlation

Lesson 3.4 More about Correlation

Lesson 3.5 Regression Lines

Lesson 3.6 The Least-Squares Regression Line

Lesson 3.7 Assessing a Regression Model

**Chapter 4 Collecting Data**

Lesson 4.1 Introduction to Data Collection

Lesson 4.2 Sampling: Good and Bad

Lesson 4.3 Sampling and Surveys

Lesson 4.4 Inference for Sampling

Lesson 4.5 Observational Studies and Experiments

Lesson 4.6 How to Experiment Well

Lesson 4.7 Inference for Experiments

Lesson 4.8 Using Studies Wisely

**Chapter 5 Probability**

Lesson 5.1 Randomness, Probability, and Simulation

Lesson 5.2 Basic Probability Rules

Lesson 5.3 Two-Way Tables and Venn Diagrams

Lesson 5.4 Conditional Probability and Independence

Lesson 5.5 The General Multiplication Rule and Tree Diagrams

Lesson 5.6 The Multiplication Rule for Independent Events

Lesson 5.7 The Multiplication Counting Principle and Permutations

Lesson 5.8 Combinations and Probability

**Chapter 6 Random Variables**

Lesson 6.1 Two Types of Random Variables

Lesson 6.2 Analyzing Discrete Random Variables

Lesson 6.3 Binomial Random Variables

Lesson 6.4 Analyzing Binomial Random Variables

Lesson 6.5 Normal Approximation to Binomial Distributions

**Chapter 7 Sampling Distributions **Lesson 7.1 What Is a Sampling Distribution?

Lesson 7.2 Sampling Distributions: Center and Variability

Lesson 7.3 The Sampling Distribution of a Sample Proportion

Lesson 7.4 The Sampling Distribution of a Sample Mean

Lesson 7.5 The Central Limit Theorem

**Chapter 8 Estimating a Parameter **Lesson 8.1 The Idea of a Confidence Interval

Lesson 8.2 What Affects the Margin of Error?

Lesson 8.3 Estimating a Proportion

Lesson 8.4 Confidence Intervals for a Proportion

Lesson 8.5 Estimating a Mean

Lesson 8.6 Confidence Intervals for a Mean

**Chapter 9 Testing a Claim** Lesson 9.1 The Idea of a Significance Test

Lesson 9.2 Significance Tests and Decision Making

Lesson 9.3 Testing a Claim about a Proportion

Lesson 9.4 Significance Tests for a Proportion

Lesson 9.5 Testing a Claim about a Mean

Lesson 9.6 Significance Tests for a Mean

**Chapter 10 Comparing Two Populations or Treatments**

Lesson 10.1 Estimating a Difference Between Two Proportions

Lesson 10.2 Testing a Claim about a Difference Between Two Proportions

Lesson 10.3 Estimating a Difference Between Two Means

Lesson 10.4 Testing a Claim about a Difference Between Two Means

Lesson 10.5 Paired Data: Estimating a Mean Difference

Lesson 10.6 Paired Data: Testing a Claim about a Mean Difference

**Chapter 11 Inference for Distributions and Relationships**

Lesson 11.1 Testing the Distribution of a Categorical Variable

Lesson 11.2 Chi-Square Tests for Goodness of Fit

Lesson 11.3 Testing the Relationship Between Two Categorical Variables

Lesson 11.4 Chi-Square Tests for Association

Lesson 11.5 Estimating the Slope of a Least-Squares Regression Line

Lesson 11.6 Testing a Claim about the Slope of a Least-Squares Regression Line

Solutions

Glossary/Glosario

Notes and Data Sources

Index

Table A Standard Normal Probabilities

Table B t Distribution Critical Values

Table C Chi-Square Distribution Critical Values

Table D Random Digits

Look Inside

**Statistics and Probability with Applications (High School)**

Fourth Edition| 2021

Daren Starnes; Josh Tabor; Luke Wilcox

## Authors

### Daren S. Starnes

**Daren S. Starnes** is Mathematics Department Chair and holds the Robert S. and Christina Seix Dow Distinguished Master Teacher Chair in Mathematics at The Lawrenceville School near Princeton, New Jersey. He earned his MA in Mathematics from the University of Michigan and his BS in Mathematics from the University of North Carolina at Charlotte. Daren is also an alumnus of the North Carolina School of Science and Mathematics. Daren has led numerous one-day and weeklong AP® Statistics institutes for new and experienced teachers, and he has been a Reader, Table Leader, and Question Leader for the AP® Statistics exam since 1998. Daren is a frequent speaker at local, state, regional, national, and international conferences. He has written articles for *The Mathematics Teacher* and *CHANCE* magazine. From 2004 to 2009, Daren served on the ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability (which he chaired in 2009). While on the committee, he edited the Guidelines for Assessment and Instruction in Statistics Education (GAISE) pre-K–12 report and coauthored (with Roxy Peck) *Making Sense of Statistical Studies*, a capstone module in statistical thinking for high school students. Daren is also coauthor of the popular on-level text *Statistics and Probability with Applications*.

### Josh Tabor

**Josh Tabor** has enjoyed teaching on-level and AP® Statistics to high school students for more than 23 years, most recently at his alma mater, Canyon del Oro High School in Oro Valley, Arizona. He received a BS in Mathematics from Biola University, in La Mirada, California. In recognition of his outstanding work as an educator, Josh was named one of the five finalists for Arizona Teacher of the Year in 2011. He is a past member of the AP® Statistics Development Committee (2005–2009) and has been a Reader, Table Leader, and Question Leader at the AP® Statistics Reading since 1999. In 2013, Josh was named to the SAT® Mathematics Development Committee. Each year, Josh leads one-week AP® Summer Institutes and College Board workshops around the world and frequently speaks at local, national, and international conferences. In addition to teaching and speaking, Josh has published articles in *The American Statistician*, *The Mathematics Teacher*, *STATS Magazine*, and *The Journal of Statistics Education*. He is the coauthor with Daren Starnes of two other popular statistics textbooks, *The Practice of Statistics for the AP® Exam*, Sixth Edition, and *Statistics and Probability with Applications*, Third Edition, for on-level statistics. Outside of work, Josh enjoys gardening, traveling, and playing board games with his family.

### Luke Wilcox

**Luke Wilcox**is a National Board Certified teacher who has spent his 20-year teaching career at East Kentwood High School, the most diverse public high school in the state of Michigan. His teaching as been recognized with the 2013 Presidential Award and the 2018 Michigan Teacher of the Year award, each giving him the opportunity to visit the White House to meet the president. Luke is the author of the Annotated Teacher’s Edition for The Practice of Statistics, where he offers valuable insights gathered from his own classroom teaching experiences, as well as from his participation as a Reader and Table Leader at the AP® Statistics Reading. Luke also supports teachers through a variety of in-person and online workshops, as well as being a frequent presenter at conferences. To further help statistics teachers, Luke co-developed the website statsmedic.com, which is positively transforming statistics instruction in classrooms around the country. Luke leads his students with an Experience First, Formalize Later approach to teaching statistics—in which students engage in the mathematical thinking and reasoning before being provided algorithmic formulas and definitions. In his spare time, Luke enjoys traveling with his wife and two kids, running, and eating tacos.

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**Statistics and Probability with Applications (High School)**

Fourth Edition| 2021

Daren Starnes; Josh Tabor; Luke Wilcox

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**Statistics and Probability with Applications (High School)**

Fourth Edition| 2021

Daren Starnes; Josh Tabor; Luke Wilcox

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